Investigating multiscale phenomena in machining: the effect of cutting-force distribution along the tool’s rake face on process stability

Regenerative machine tool chatter is investigated in a nonlinear single-degree-of-freedom model of turning processes. The nonlinearity arises from the dependence of the cutting-force magnitude on the chip thickness. The cutting-force is modeled as the resultant of a force system distributed along the rake face of the tool. It introduces a distributed delay in the governing equations of the system in addition to the well-known regenerative delay, which is often referred to as the short regenerative effect. The corresponding stability lobe diagrams are depicted, and it is shown that a subcritical Hopf bifurcation occurs along the stability limits in the case of realistic cutting-force distributions. Due to the subcriticality a so-called unsafe zone exists near the stability limits, where the linearly stable cutting process becomes unstable to large perturbations. Based on center-manifold reduction and normal form calculations analytic formulas are obtained to estimate the size of the unsafe zone.Copyright © 2015 by ASME

[1]  Jokin Munoa,et al.  Identification of cutting force characteristics based on chatter experiments , 2011 .

[2]  H. Chandrasekaran,et al.  MODELING TOOL STRESSES AND TEMPERATURE EVALUATION IN TURNING USING FINITE ELEMENT METHOD , 1998 .

[3]  Yung C. Shin,et al.  A comprehensive chatter prediction model for face turning operation including tool wear effect , 2002 .

[4]  Gábor Stépán,et al.  Semi-Discretization for Time-Delay Systems: Stability and Engineering Applications , 2011 .

[5]  Eckart Uhlmann,et al.  Chatter frequencies of micromilling processes: Influencing factors and online detection via piezoactuators , 2012 .

[6]  R. E. Wilson,et al.  Estimates of the bistable region in metal cutting , 2008, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[7]  Matthew A. Davies,et al.  NONLINEAR DYNAMICS MODEL FOR CHIP SEGMENTATION IN MACHINING , 1997 .

[8]  I. Yellowley,et al.  Stress distributions on the rake face during orthogonal machining , 1994 .

[9]  Frederick Winslow Taylor,et al.  On The Art Of Cutting Metals.pdf , 2017 .

[10]  Matthew A. Davies,et al.  On repeated adiabatic shear band formation during high-speed machining , 2002 .

[11]  B. Hassard,et al.  Theory and applications of Hopf bifurcation , 1981 .

[12]  F. Ismail,et al.  Experimental investigation of process damping nonlinearity in machining chatter , 2010 .

[13]  S. A. Tobias,et al.  Theory of finite amplitude machine tool instability , 1984 .

[14]  P. Wright,et al.  Stress analysis in machining with the use of sapphire tools , 1987, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[15]  Tony Atkins,et al.  Prediction of sticking and sliding lengths on the rake faces of tools using cutting forces , 2015 .

[16]  Zoltán Pálmai,et al.  Chip formation as an oscillator during the turning process , 2009 .

[17]  W. Graham,et al.  Determination of rake face stress distribution in orthogonal machining , 1982 .

[18]  Jon Rigelsford,et al.  Manufacturing Automation: Metal Cutting Mechanics, Machine Tool Vibrations, and CNC Design , 2004 .

[19]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[20]  J. Hale.  Theory of Functional Differential Equations , 1977 .